As a result of crossing the rectangle from one vertex to the opposite vertex we get a right triangle, like this:
With right triangles, we can use the trigonometric ratios:
[tex]\begin{gathered} \sin \theta=\frac{oc}{h} \\ \cos \theta=\frac{ac}{h} \end{gathered}[/tex]
Where h is the length of the hypotenuse of the triangle, oc is the opposite leg and ac is the adjacent leg.
By taking θ as the angle whose measure equals 30°, we get:
[tex]\begin{gathered} \sin \theta=\frac{GT}{GA} \\ \cos \theta=\frac{AT}{GA} \end{gathered}[/tex]
From the sine function, we can replace 30° for θ and 60 for GT, then solving for GA, we get:
[tex]\begin{gathered} \sin 30=\frac{60}{GA} \\ \sin 30\times GA=\frac{60}{GA}\times GA \\ \sin 30\times GA=60\times\frac{GA}{GA} \\ \sin 30\times GA=60\times1 \\ \sin 30\times GA=60 \\ \frac{\sin30}{\sin30}\times GA=\frac{60}{\sin30} \\ 1\times GA=\frac{60}{\sin30} \\ GA=\frac{60}{\sin30} \\ GA=120 \end{gathered}[/tex]
Then, GA equals 120 cm.
Similarly, by means of the trigonometric function cosine, we get:
[tex]\begin{gathered} \cos 30=\frac{AT}{120} \\ \cos 30\times120=\frac{AT}{120}\times120 \\ \cos 30\times120=AT\times\frac{120}{120} \\ \cos 30\times120=AT\times1 \\ AT=\cos 30\times120 \\ AT=60\sqrt[]{3} \end{gathered}[/tex]
Then the side AT has a length of 60√3 cm (about 104 cm)
